Easiest Way to Join Meshes
Since you are asking about the "easiest way"...

In my opinion, the easiest way to deal with those situations is by not creating them in the first place (unfortunately minecraft and other apps seem to have created unnecessary problems when it comes to modeling, by thinking in boxes that get added and somehow have to be connected. You have to think outside the box...).

If you know that those parts have to be connected, create them as connected elements from the start. 

In this case create a base mesh, scale, add a couple of loop cuts and extrude. 

The shape of your object is the result of it's topology. Topology shouldn't be an afterthought